Having lifted the FA Cup at the weekend, Wigan's joy turned to despair as their eight-year stay in the Premier League was brought to an end by a 4-1 defeat at Emirates Stadium.
The Gunners were pegged back to 1-1 as Shaun Maloney responded to Lukas Podolski's opener, but Theo Walcott struck in the 63rd minute and there were further goals for Podolski and Aaron Ramsey.
Wenger told Sky Sports: "I am happy that we won the game. We had a good start but then became a bit conservative and got caught just before half-time.
"At 1-1, Wojciech made a good save and then in the last 20 minutes the fact that we maintained the pace, and they were tired from the FA Cup final, gave us a big win.
"On the break, Walcott's goal was certainly decisive. From then on, you felt that for Wigan it was becoming difficult."
Wenger feels Wigan's relegation will be a loss to the Premier League as he admires the way they play.
He said: "You want to congratulate Wigan and you feel sorry for them, because with the quality of football they play it is sad that they go down.
"Wigan are a good footballing side with intelligent players and it is difficult to understand, but that is the harsh truth of the game."
The result lifted Arsenal back into fourth place and they will clinch UEFA Champions League qualification with another win at Newcastle on Sunday.
Wenger is pleased that his side will not have to rely on any favours from elsewhere and is in confident mood after a nine-match unbeaten run.
"It has always been in our hands since recently," he noted. "It is another big game on Sunday and we want to prepare for that and give it all again because we are on a very strong run.
"If you look at the number of wins we have, that is quite positive."